This paper describes the spatial stability characteristics of compressible elliptic jets. Solutions are obtained to the compressible, inviscid, linearized equations of motion; the compressible Rayleigh equation. Separable forms of solution are obtained in the jet potential core and outside the jet in terms of series of Mathieu and modified Mathieu functions. These solutions are matched using a shooting method that integrates the Rayleigh equation through the region of nonuniform velocity and density. Four classes of instability modes are studied; modes that are odd or even about the jet’s major and minor axes. Their stability characteristics are documented for a range of jet aspect ratios, jet Mach numbers and temperatures, and azimuthal distributions of jet shear layer thickness. The growth rates of the modes are found to depend on their class and the jet thickness on the major and minor axes. The mode that ‘‘flaps’’ about the jet major axis is found to be the most unstable as the jet Mach number or aspect ratio increases. ©1995 American Institute of Physics.